相对于子范畴的同伦分解的存在性

The Existence of Homotopy Resolutions Relative to the Subcategory

本文证明了在相对于子范畴的情形下上有界复形的同伦分解的存在性,推广了经典的复形的同伦分解,是使得相对导出范畴具有可操作性的基础.进一步,证明了在R-模范畴和相对于特殊子范畴的情形下,任意无界复形的同伦分解的存在性.最后,建立了同伦范畴和相对导出范畴的(余)局部化序列.

Let be a subcategory of an abelian category A.We proceed by generalizing the homotopy resolutions of complexes to the relative version,which is important basis making the relative derived category operational.We prove that every bounded above complex has a dg X resolution.Furthermore,we also show that the existence of resolutions for any unbounded complex when A=R-Mod and is a particular subcategory.Finally,we establish a colocalization sequence of the homotopy category K(A) involving the relative derived category under some condition.